about summary refs log tree commit diff
path: root/langfassung/master.aux
diff options
context:
space:
mode:
authorhanemile <emile.hansmaennel@gmail.com>2018-02-09 13:43:39 +0100
committerhanemile <emile.hansmaennel@gmail.com>2018-02-09 13:43:39 +0100
commit05b7139e8e9fdb01b24b3fa26260f1c5fdbb85d9 (patch)
tree957017d0e3efe82164887c754c34019a979ebdd6 /langfassung/master.aux
parent1b1e0bfd1a5e9d88886b58b0d4db05cafbb36365 (diff)
update the things that happend after the document was handed in
Diffstat (limited to 'langfassung/master.aux')
-rwxr-xr-x[-rw-r--r--]langfassung/master.aux349
1 files changed, 319 insertions, 30 deletions
diff --git a/langfassung/master.aux b/langfassung/master.aux
index 50fae93..0a6be6c 100644..100755
--- a/langfassung/master.aux
+++ b/langfassung/master.aux
@@ -23,62 +23,351 @@
 \@writefile{lof}{\select@language{ngerman}}
 \@writefile{lot}{\select@language{ngerman}}
 \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces \relax }}{1}{figure.caption.1}}
+\@setckpt{docs/1_kurzfassung}{%
+\setcounter{page}{1}
+\setcounter{equation}{0}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
+\setcounter{enumiv}{0}
+\setcounter{footnote}{0}
+\setcounter{mpfootnote}{0}
+\setcounter{part}{0}
+\setcounter{section}{0}
+\setcounter{subsection}{0}
+\setcounter{subsubsection}{0}
+\setcounter{paragraph}{0}
+\setcounter{subparagraph}{0}
+\setcounter{figure}{1}
+\setcounter{table}{0}
+\setcounter{parentequation}{0}
+\setcounter{Item}{0}
+\setcounter{Hfootnote}{0}
+\setcounter{bookmark@seq@number}{0}
+\setcounter{IncludeDepth}{0}
+\setcounter{ContinuedFloat}{0}
+\setcounter{lstnumber}{1}
+\setcounter{section@level}{0}
+\setcounter{lstlisting}{0}
+}
 \@writefile{toc}{\contentsline {section}{\numberline {1}Einleitung}{2}{section.1}}
 \newlabel{Einleitung}{{1}{2}{Einleitung}{section.1}{}}
+\@auxtag{docs/2_einleitung}{%
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Themen}{2}{subsection.1.1}}
+}
+\@auxtag{docs/2_einleitung}{%
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Motivation}{2}{subsection.1.2}}
+}
+\@setckpt{docs/2_einleitung}{%
+\setcounter{page}{2}
+\setcounter{equation}{0}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
+\setcounter{enumiv}{0}
+\setcounter{footnote}{2}
+\setcounter{mpfootnote}{0}
+\setcounter{part}{0}
+\setcounter{section}{1}
+\setcounter{subsection}{2}
+\setcounter{subsubsection}{0}
+\setcounter{paragraph}{0}
+\setcounter{subparagraph}{0}
+\setcounter{figure}{1}
+\setcounter{table}{0}
+\setcounter{parentequation}{0}
+\setcounter{Item}{0}
+\setcounter{Hfootnote}{2}
+\setcounter{bookmark@seq@number}{3}
+\setcounter{IncludeDepth}{0}
+\setcounter{ContinuedFloat}{0}
+\setcounter{lstnumber}{1}
+\setcounter{section@level}{2}
+\setcounter{lstlisting}{0}
+}
 \@writefile{toc}{\contentsline {section}{\numberline {2}Hauptteil}{3}{section.2}}
 \newlabel{Hauptteil}{{2}{3}{Hauptteil}{section.2}{}}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Generierung von elliptischen Galaxien}{3}{subsection.2.1}}
+}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.1}Das Navarro-Frenk-White Profil}{3}{subsubsection.2.1.1}}
+}
 \newlabel{eq:NFW_profile}{{1}{3}{Das Navarro-Frenk-White Profil}{equation.2.1}{}}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.2}Random Sampling}{3}{subsubsection.2.1.2}}
+}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Eine mit dem NFW-profil und der Random Sampling Methode generierte Galaxie\relax }}{4}{figure.caption.3}}
+}
 \providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
 \newlabel{fig:galaxy}{{2}{4}{Eine mit dem NFW-profil und der Random Sampling Methode generierte Galaxie\relax }{figure.caption.3}{}}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  Die Rho Funktion im Intervall \( [~0~;~10^7 ~] \) geplottet mithilfe von Logarithmischen Achsen.   Die x-Achse beschreibt die Entfernung zum Mittelpunkt der Galaxie   Die y-Achse beschreibt die Warscheinlichkeit das ein Stern generiert wird \relax }}{4}{figure.caption.4}}
+}
 \newlabel{fig:rho}{{3}{4}{Die Rho Funktion im Intervall \( [~0~;~10^7 ~] \) geplottet mithilfe von Logarithmischen Achsen. \\ Die x-Achse beschreibt die Entfernung zum Mittelpunkt der Galaxie \\ Die y-Achse beschreibt die Warscheinlichkeit das ein Stern generiert wird \relax }{figure.caption.4}{}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.2}Random Sampling}{5}{subsubsection.2.1.2}}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.3}Lookup Tabellen}{5}{subsubsection.2.1.3}}
+}
 \newlabel{subsec:lookup}{{2.1.3}{5}{Lookup Tabellen}{subsubsection.2.1.3}{}}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Generierung eines Dunkle-Materie Halos durch Anpassung des NFW-Profils}{5}{subsection.2.2}}
+}
 \newlabel{eq:dark_matter}{{3}{5}{Generierung eines Dunkle-Materie Halos durch Anpassung des NFW-Profils}{equation.2.3}{}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Stauchung und Streckung der Galaxie}{6}{subsection.2.3}}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Stauchung und Streckung der Galaxie}{5}{subsection.2.3}}
+}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Rechenaufwand}{6}{subsection.2.4}}
+}
 \newlabel{subsec:big_o}{{2.4}{6}{Rechenaufwand}{subsection.2.4}{}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Beschleunigung der Generation}{7}{subsection.2.5}}
-\newlabel{subsec:speeding_things_up}{{2.5}{7}{Beschleunigung der Generation}{subsection.2.5}{}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.1}Lookuptable}{7}{subsubsection.2.5.1}}
-\newlabel{subsec:lookuptable}{{2.5.1}{7}{Lookuptable}{subsubsection.2.5.1}{}}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Beschleunigung der Generation}{6}{subsection.2.5}}
+}
+\newlabel{subsec:speeding_things_up}{{2.5}{6}{Beschleunigung der Generation}{subsection.2.5}{}}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.1}Lookuptable}{6}{subsubsection.2.5.1}}
+}
+\newlabel{subsec:lookuptable}{{2.5.1}{6}{Lookuptable}{subsubsection.2.5.1}{}}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.2}Mehr Rechenleistung!}{7}{subsubsection.2.5.2}}
+}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {paragraph}{\nonumberline Amazon Web Services}{7}{section*.5}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.3}Nichts in der Konsole ausgeben}{8}{subsubsection.2.5.3}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Nutzung eines neuronalen Netzes zum unbeaufsichtigten generieren von Galaxien}{8}{subsection.2.6}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}Aufbau des neuronalen Netzes}{8}{subsubsection.2.6.1}}
+}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.3}Nichts in der Konsole ausgeben}{7}{subsubsection.2.5.3}}
+}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Nutzung eines neuronalen Netzes zum unbeaufsichtigten generieren von Galaxien}{7}{subsection.2.6}}
+}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}Aufbau des neuronalen Netzes}{7}{subsubsection.2.6.1}}
+}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {paragraph}{\nonumberline Neuronen und Synapsen}{8}{section*.6}}
+}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Spiralgalaxien}{9}{subsection.2.7}}
+}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.1}Das n-K\IeC {\"o}rper Problem}{9}{subsubsection.2.7.1}}
-\newlabel{eq:n-body-2nd}{{10}{10}{Das n-Körper Problem}{equation.2.10}{}}
-\newlabel{eq:hamilton}{{11}{10}{Das n-Körper Problem}{equation.2.11}{}}
+}
+\newlabel{eq:n-body-2nd}{{10}{9}{Das n-Körper Problem}{equation.2.10}{}}
+\newlabel{eq:hamilton}{{11}{9}{Das n-Körper Problem}{equation.2.11}{}}
+\@auxtag{docs/3_hauptteil}{%
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.2}Unterteilung des Vektorraumes in verschiedene Zellen}{10}{subsubsection.2.7.2}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.3}Berechnung der wirkenden Kr\IeC {\"a}fte}{11}{subsubsection.2.7.3}}
-\newlabel{eq:gravitation_law}{{16}{11}{Berechnung der wirkenden Kräfte}{equation.2.16}{}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Masse der Sterne}{11}{section*.7}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Abstand der Sterne}{11}{section*.8}}
-\newlabel{eq:pytagoras}{{17}{11}{Abstand der Sterne}{equation.2.17}{}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.8}Weiteres}{11}{subsection.2.8}}
-\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Eine Spiralgalaxie generiert mithilfe von Daten aus dem Max-Plank-Institut in Heidelberg\relax }}{12}{figure.caption.9}}
-\newlabel{fig:spiralgalaxy}{{4}{12}{Eine Spiralgalaxie generiert mithilfe von Daten aus dem Max-Plank-Institut in Heidelberg\relax }{figure.caption.9}{}}
-\@writefile{toc}{\contentsline {section}{\numberline {3}Ergebnisse}{12}{section.3}}
-\newlabel{ergebnisse}{{3}{12}{Ergebnisse}{section.3}{}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Simulations Geschwindigkeit}{12}{subsection.3.1}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Lookuptabellen Geschwindigkeit}{12}{subsection.3.2}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Fazit}{13}{subsection.3.3}}
-\@writefile{toc}{\contentsline {section}{\numberline {4}Quellen und Hilfen}{14}{section.4}}
-\newlabel{quellen}{{4}{14}{Quellen und Hilfen}{section.4}{}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{14}{section*.11}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tim Tugendhat}{14}{section*.12}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{14}{section*.13}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{14}{section*.14}}
+}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.3}Berechnung der wirkenden Kr\IeC {\"a}fte}{10}{subsubsection.2.7.3}}
+}
+\newlabel{eq:gravitation_law}{{16}{10}{Berechnung der wirkenden Kräfte}{equation.2.16}{}}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Masse der Sterne}{10}{section*.7}}
+}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Abstand der Sterne}{10}{section*.8}}
+}
+\newlabel{eq:pytagoras}{{17}{10}{Abstand der Sterne}{equation.2.17}{}}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.8}Weiteres}{10}{subsection.2.8}}
+}
+\@setckpt{docs/3_hauptteil}{%
+\setcounter{page}{10}
+\setcounter{equation}{17}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
+\setcounter{enumiv}{0}
+\setcounter{footnote}{3}
+\setcounter{mpfootnote}{0}
+\setcounter{part}{0}
+\setcounter{section}{2}
+\setcounter{subsection}{8}
+\setcounter{subsubsection}{0}
+\setcounter{paragraph}{0}
+\setcounter{subparagraph}{0}
+\setcounter{figure}{4}
+\setcounter{table}{0}
+\setcounter{parentequation}{0}
+\setcounter{Item}{0}
+\setcounter{Hfootnote}{3}
+\setcounter{bookmark@seq@number}{22}
+\setcounter{IncludeDepth}{0}
+\setcounter{ContinuedFloat}{0}
+\setcounter{lstnumber}{15}
+\setcounter{section@level}{2}
+\setcounter{lstlisting}{0}
+}
+\@auxtag{docs/3_hauptteil}{%
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Eine Spiralgalaxie generiert mithilfe von Daten aus dem Max-Plank-Institut in Heidelberg\relax }}{11}{figure.caption.9}}
+}
+\newlabel{fig:spiralgalaxy}{{4}{11}{Eine Spiralgalaxie generiert mithilfe von Daten aus dem Max-Plank-Institut in Heidelberg\relax }{figure.caption.9}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Ergebnisse}{11}{section.3}}
+\newlabel{ergebnisse}{{3}{11}{Ergebnisse}{section.3}{}}
+\@auxtag{docs/4_ergebnisse}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Simulations Geschwindigkeit}{11}{subsection.3.1}}
+}
+\@auxtag{docs/4_ergebnisse}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Lookuptabellen Geschwindigkeit}{11}{subsection.3.2}}
+}
+\@auxtag{docs/4_ergebnisse}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Fazit}{11}{subsection.3.3}}
+}
+\@setckpt{docs/4_ergebnisse}{%
+\setcounter{page}{12}
+\setcounter{equation}{17}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
+\setcounter{enumiv}{0}
+\setcounter{footnote}{3}
+\setcounter{mpfootnote}{0}
+\setcounter{part}{0}
+\setcounter{section}{3}
+\setcounter{subsection}{3}
+\setcounter{subsubsection}{0}
+\setcounter{paragraph}{0}
+\setcounter{subparagraph}{0}
+\setcounter{figure}{4}
+\setcounter{table}{0}
+\setcounter{parentequation}{0}
+\setcounter{Item}{0}
+\setcounter{Hfootnote}{3}
+\setcounter{bookmark@seq@number}{26}
+\setcounter{IncludeDepth}{0}
+\setcounter{ContinuedFloat}{0}
+\setcounter{lstnumber}{15}
+\setcounter{section@level}{2}
+\setcounter{lstlisting}{0}
+}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Quellen und Hilfen}{13}{section.4}}
+\newlabel{quellen}{{4}{13}{Quellen und Hilfen}{section.4}{}}
+\@auxtag{docs/5_quellen}{%
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{13}{section*.11}}
+}
+\@auxtag{docs/5_quellen}{%
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tim Tugendhat}{13}{section*.12}}
+}
+\@auxtag{docs/5_quellen}{%
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{13}{section*.13}}
+}
+\@auxtag{docs/5_quellen}{%
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{13}{section*.14}}
+}
+\@setckpt{docs/5_quellen}{%
+\setcounter{page}{13}
+\setcounter{equation}{17}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
+\setcounter{enumiv}{0}
+\setcounter{footnote}{3}
+\setcounter{mpfootnote}{0}
+\setcounter{part}{0}
+\setcounter{section}{4}
+\setcounter{subsection}{0}
+\setcounter{subsubsection}{0}
+\setcounter{paragraph}{0}
+\setcounter{subparagraph}{0}
+\setcounter{figure}{4}
+\setcounter{table}{0}
+\setcounter{parentequation}{0}
+\setcounter{Item}{0}
+\setcounter{Hfootnote}{3}
+\setcounter{bookmark@seq@number}{27}
+\setcounter{IncludeDepth}{0}
+\setcounter{ContinuedFloat}{0}
+\setcounter{lstnumber}{15}
+\setcounter{section@level}{4}
+\setcounter{lstlisting}{0}
+}
+\@writefile{toc}{\contentsline {section}{\numberline {5}Nach der Abgabe...}{14}{section.5}}
+\newlabel{nach_der_abgabe}{{5}{14}{Nach der Abgabe..}{section.5}{}}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Spiralgalaxien}{14}{subsection.5.1}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Using Object Oriented Programming (OOP) techniques}{14}{subsection.5.2}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1}Initialisation}{14}{subsubsection.5.2.1}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Generation of new stars}{14}{subsection.5.3}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Printing all the coordinates}{14}{subsection.5.4}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Calculating the Forces acting between the Stars}{14}{subsection.5.5}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Calculating the forces acting between each star in the galaxy and each other star}{15}{subsection.5.6}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.7}Printing all the individual forces}{15}{subsection.5.7}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.8}Spherical cells}{15}{subsection.5.8}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.8.1}Testing if a point is inside or outside a sphere}{15}{subsubsection.5.8.1}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.8.2}Testing if a star is inside or outside of a sphere for a whole galaxy}{15}{subsubsection.5.8.2}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.8.3}Generate the position of the spheres}{15}{subsubsection.5.8.3}}
+}
+\newlabel{sphere_distance}{{20}{15}{Generate the position of the spheres}{equation.5.20}{}}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces The Alignment of the spheres  Left: The perfect alignment covering the complete space  Right: A previously generated alignment using small spheres to cover the missing space \relax }}{16}{figure.caption.15}}
+}
+\newlabel{sphere_alignment}{{5}{16}{The Alignment of the spheres\\ Left: The perfect alignment covering the complete space\\ Right: A previously generated alignment using small spheres to cover the missing space \relax }{figure.caption.15}{}}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.8.4}The radius of the spheres}{16}{subsubsection.5.8.4}}
+}
+\newlabel{sphere_radius}{{21}{16}{The radius of the spheres}{equation.5.21}{}}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.8.5}Calculate the forces acting on the spheres}{16}{subsubsection.5.8.5}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.8.6}Calculate the forces acting on all the spheres together}{17}{subsubsection.5.8.6}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.8.7}Benchmarks}{17}{subsubsection.5.8.7}}
+}
+\@auxtag{docs/6_abgabe}{%
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.9}Calculate the Position of a Star after a timestep}{17}{subsection.5.9}}
+}
+\@setckpt{docs/6_abgabe}{%
+\setcounter{page}{17}
+\setcounter{equation}{21}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
+\setcounter{enumiv}{0}
+\setcounter{footnote}{3}
+\setcounter{mpfootnote}{0}
+\setcounter{part}{0}
+\setcounter{section}{5}
+\setcounter{subsection}{9}
+\setcounter{subsubsection}{0}
+\setcounter{paragraph}{0}
+\setcounter{subparagraph}{0}
+\setcounter{figure}{5}
+\setcounter{table}{0}
+\setcounter{parentequation}{0}
+\setcounter{Item}{0}
+\setcounter{Hfootnote}{3}
+\setcounter{bookmark@seq@number}{45}
+\setcounter{IncludeDepth}{0}
+\setcounter{ContinuedFloat}{0}
+\setcounter{lstnumber}{15}
+\setcounter{section@level}{2}
+\setcounter{lstlisting}{0}
+}
 \global\@namedef{scr@dte@section@lastmaxnumwidth}{9.89993pt}
 \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{16.7777pt}
 \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{24.55545pt}